People gather during a rally in Kiev's Maidan Nezalezhnosti, or 'independence square', last month. Photograph: Sergei Chuzavkov/AP

The urban planners of the Soviet Union excelled at creating the spectacle of revolution. Huge wide boulevards for the marching public, culminating in immense squares for assembly and rally where colossal statues of Lenin exhorted in absentia. Long after the collapse of the USSR, they often remain at the heart of cities from Berlin to Moscow. But what happens to places like these when an actual urban insurrection hits them?

The overthrow of Viktor Yanukovych after three months of increasingly violent street demonstrations took place in an extremely Soviet urban setpiece, in Kiev. The 'EuroMaidan' movement is even named after the Stalinist square at its heart, Maidan Nezalezhnosti (Independence Square), as if the place is as important as the movement's demands. Walking around the city, you could see why.

Four weeks after Yanukovych had fled the city, most of Kiev appeared much as normal, bar a certain unease and some unusually vehement graffiti. Straying into the city's central Soviet showpiece, however, the barricades and encampments were still in place, making their bid for permanence. It was exactly this area (the grandiose boulevard of the Kreschatyk, the government buildings on Hrushevsky Street, and Maidan Nezalezhnosti itself – all of them grand projects of the Stalin era) where the insurrection that overthrew Yanukovych occurred, where it is now commemorated, and from where it may yet continue.

The great irony, of course, is that this sort of planning originated as a way of deterring revolution.The Stalinist approach was a supercharged, steroidal version of that introduced under Baron Haussmann in Napoleon III's Paris. Famously, in order to create free lines of fire and to discourage the making of barricades, Haussmann carved out centrifugal spaces like the Place de la Republique and the various long, straight, wide boulevards.

From the 1930s on, Stalin increasingly resembled a particularly despotic student of Haussmann, evidently ignoring Marx's loathing for the planner who "replaced historic Paris with the Paris of the sightseer". Tverskaya in Moscow, Karl-Marx-Allee in Berlin and Marszalkowska in Warsaw are the best known of these spectacular arteries, or magistrale, lined with palatial apartments and leading to vast public assembly points and parade grounds like Red Square, Alexanderplatz and Plac Defilad.

But the post-war rebuilding of Kiev's Kreschatyk boulevard and the October Revolution Square (as Maidan then was known) was perhaps the most staggeringly opulent of them all. Beginning at the early 20th-century Bessarabsky market, it sweeps through the historic centre with a prickly skyline of spires and obelisks, its façades coated in decorative tiles, to a 1949 design by architect Anatoly Dobrovolsky. Created to support Stalin's case for Soviet Ukraine's seat in the UN, the main monument, as ever, was a massive granite Lenin, flanked by revolutionaries, as a memorial to the October 1917 insurrection. Whereas Haussmann wanted to stop revolution, Stalin and his successors constantly appealed to its memory.

Independence Square back when it was known as October Revolution Square – one of the most opulent examples of Stalinist planning. Photograph: Socialism Expo

Remnants of a revolution

At Maidan Nezalezhnosti metro station, there are bronze plaques on the walls dedicated to 1917, a remnant from when this was October Revolution Square station. Making our way out, we found half the exits still blocked by barricades made from tyres, sandbags, paving stones and furniture. Outside was the aftermath of a real urban revolution.

Regardless of the cant about a 'coup' in Kiev, it's clear that in central and western Ukraine at least, this was hardly some backroom deal at the top; rather it was the consequence of a mass, public, violent, collective act. It is impossible to visit Maidan and think otherwise.

My partner and I were last in Kiev three years ago; returning last week, we were astonished at how different Maidan looked. Pedestrian pathways ran through encampments and barricades four foot high. The ground was charred, the paving stones unreplaced. Armoured cars blared out rousing songs as the temporary stage was taken by an Orthodox priest.

The trade union building, recently occupied by the revolutionaries, was now a charred husk with most of its windows blown out, while McDonald's, having become a makeshift mental hospital at the close of the protests, was now a McDonald's again – to the regret of our friends who worried that the square would eventually revert back to being an empty, corporate plaza rather than the space it became during the protests (although apparently, the underground Globus shopping mall below Maidan stayed open throughout).

Elsewhere, the transformation was more subtle. Walking down 19th-century Taras Shevchenko boulevard, the turn into the Kreschatyk was denoted by the plinth of the Lenin statue – toppled last December and caked in graffiti, either in cryptic, esoteric far-right symbols or with the more obvious "glory to Ukraine".

The Kreschatyk boulevard was interrupted after one block by tents and surviving barricades in front of towering Stalinist castles. Grand archways leading to the side streets were blocked with tyres. The protesters had used the qualities of the Stalinist architecture – flights of steps, triumphal arches, wide streets and huge squares – to their advantage, blocking potential entry points and congregating on the free, open spaces. Kiev City Hall was graffiti covered, and occupying a mobile phone shop next to the branch of Oggi were the far-right paramilitary alliance Pravy Sektor (Right Sector).

It seems unfair to judge 'EuroMaidan' as a movement on this, its aftermath, when Russia's annexation of Crimea has ramped up the tension so – but the political content in central Kiev now is not pretty. We saw posters calling for peace, many of the national poet and revolutionary Taras Shevchenko, a few anarchist symbols and one image of the communist poet Vladimir Mayakovsky (with the speech bubble, "Comrade Muscovite, leave Ukraine alone!") – but they were overwhelmingly outnumbered by symbols of the extreme right.

At Maidan, next to the stage, a banner showed the visage of Stepan Bandera, whose OUN-B and Ukrainian Insurgent Army (UPA) were an openly fascist partisan force during and after the second world war. Not only did they fight the Soviets, they tried their best to create a "Ukraine for Ukrainians" by cleansing it of Jews (co-operating in the 1941 Nazi pogroms in Lviv) and of Poles (massacring on their own around 100,000 Polish civilians in a campaign of 1943). We saw the UPA's red-and-black colours on the armbands of scores of men in fatigues, the words Pravy Sektor confirming their political allegiance.

Yet according to our friends here – all of them participants, all of the left – this was just one of many incarnations of Maidan, which has constantly shifted over the last few months, from a middle-class revolt to a mass popular uprising to "something like the middle ages". Certainly, the air of menace created by the armed presence of the far-right contrasted with the festive spirit we felt as countless people walked around Kreschatyk and Maidan, squeezing through the barricades to leave flowers at the memorial to the hundred protesters killed by Yanukovych's snipers, or simply to witness the place's transformation.

Their own little totalitarian state

At the end of Kreschatyk, the monumental Hotel Dnipro faces Ukrainian House (the former Lenin Museum), an early 80s, stripped-down classical building. This, apparently, was always the best part of the recent insurrection: its rotunda enclosed a shelter, library, university and cinema – plus spectacular stained-glass images of revolution above, and a real revolt below.

"I'd always hoped to see it like that," one friend said. During our visit, however, it was full of armed, armband-wearing men. "It's gone very Stanford Experiment in there," he explained. "They're setting up their own little totalitarian state."

Another friend described Pravy Sektor as "the ultimate political technology for Putin – they do his work for him and he doesn't even have to pay them". The far-right, whether these paramilitaries or the 'post-fascist' Svoboda party, part of the interim coalition government, are running extremely low in the opinion polls, but the possible fates awaiting post-revolutionary Ukraine – Russian invasion, IMF shock therapy, or yet another government of Ukrainian oligarchs – all appear practically engineered to increase their support.

An old postcard of Svobody Square in Kharkiv in eastern Ukraine. The largest Soviet square saw shootouts between pro-Russians and pro-Ukrainians last month. Photograph: Socialism Expo

Even though there are divisions within it, the support of most people in Kiev for Yanukovych's overthrow is undeniable – unlike in the densely populated, industrial eastern Ukraine, with its close economic and cultural ties to Russia. The largest of the Soviet Union's squares, the enormous Svoboda Square in the eastern city of Kharkiv, has seen battles and shootouts between 'pro-Russians' and 'pro-Ukrainians' in the last month, which, tellingly, began as a conflict over the Lenin statue in the middle of the square.

The new messages introduced by the far-right have divided what might otherwise have been a genuinely nationwide revolution. "People in eastern Ukraine make the same arguments as those in Maidan," we were told. "They hate corruption, they hate being exploited, they hate Yanukovych, they know there's a richer country next door – and they conclude for Russia rather than the EU."

In Kharkiv, there has just been an agreement that the Lenin statue will be left alone. On the empty plinth of the toppled Lenin in Kiev, surrounded by Stalinist castles and Ukrainian insurgent camps, is the original inscription: "A free Ukraine is impossible without the unity of Russian and Ukrainian workers." It's almost obscured by the scrawl, but it's there.